Solve for b: 4(b/2 + b) - 1/3 = 6b Linear Equation

Q: How can an equation have no solution?

When you simplify and get a false statement like $ -\frac{1}{3} = 0 $, it means there's no value of b that makes the original equation true. The equation is inconsistent!

Q: What's the difference between no solution and zero as a solution?

Zero as a solution means b = 0 works in the equation. No solution means no value (including zero) makes the equation true. Big difference!

Q: Did I make a mistake if I get no solution?

Not necessarily! Always double-check your algebra, but some equations genuinely have no solution. If your work is correct and you get a false statement, "no solution" is the right answer.

Q: How do I distribute 4 to the fraction correctly?

Multiply 4 by each term: $ 4 \times \frac{b}{2} = \frac{4b}{2} = 2b $ and $ 4 \times b = 4b $. Then combine: $ 2b + 4b = 6b $.

Q: What should I write as my final answer?

Write "No solution" or use the symbol $ \emptyset $ (empty set). Don't leave it blank or write "impossible" - be specific that no solution exists.

Linear Equations with No Solution

$4(\frac{b}{2}+b)-\frac{1}{3}=6b$

$b=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Open parentheses properly, multiply by each factor

00:08 We want to isolate the variable B

00:16 Divide 4 by 2

00:28 Collect like terms

00:35 Arrange the equation so that only B is on one side

00:41 Simplify what we can

00:44 We got an illogical expression, therefore there is no solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$4(\frac{b}{2}+b)-\frac{1}{3}=6b$

$b=\text{?}$

Step-by-step solution

First, we'll expand the parentheses by multiplying each term by 4:

$4\times\frac{b}{2}+4\times b-\frac{1}{3}=6b$

Let's then solve the multiplication exercise $4\times\frac{b}{2}=\frac{4b}{2}=2b$ .

Now the equation is:

$2b+4b-\frac{1}{3}=6b$

We can now combine the left-hand side between the two $b$ terms to get:

$6b-\frac{1}{3}=6b$

We'll reduce both sides by $6b$ , leaving us with:

$-\frac{1}{3}=0$

Since the result obtained is impossible, the exercise has no solution.

Final Answer

No solution

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Multiply each term inside parentheses by the outside coefficient
Technique: Combine like terms: $2b + 4b = 6b$
Check: When variables cancel and constants don't equal: no solution exists ✓

Common Mistakes

Avoid these frequent errors

Assuming every equation has a solution
Don't keep solving when you get $-\frac{1}{3} = 0$ = impossible statement! This contradictory result means the equation has no solution. Always recognize when variable terms cancel but constants don't match - this indicates no solution exists.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

How can an equation have no solution?

When you simplify and get a false statement like $-\frac{1}{3} = 0$ , it means there's no value of b that makes the original equation true. The equation is inconsistent!

What's the difference between no solution and zero as a solution?

Zero as a solution means b = 0 works in the equation. No solution means no value (including zero) makes the equation true. Big difference!

Did I make a mistake if I get no solution?

Not necessarily! Always double-check your algebra, but some equations genuinely have no solution. If your work is correct and you get a false statement, "no solution" is the right answer.

How do I distribute 4 to the fraction correctly?

Multiply 4 by each term: $4 \times \frac{b}{2} = \frac{4b}{2} = 2b$ and $4 \times b = 4b$ . Then combine: $2b + 4b = 6b$ .

What should I write as my final answer?

Write "No solution" or use the symbol $\emptyset$ (empty set). Don't leave it blank or write "impossible" - be specific that no solution exists.

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Solve for b: 4(b/2 + b) - 1/3 = 6b Linear Equation

Linear Equations with No Solution

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How can an equation have no solution?

What's the difference between no solution and zero as a solution?

Did I make a mistake if I get no solution?

How do I distribute 4 to the fraction correctly?

What should I write as my final answer?

🌟 Unlock Your Math Potential

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